Finite element analysis (FEA) is a computerized method widely used in industry to model and solve engineering problems related to complex systems such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modern digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
One of the most challenging FEA tasks is to simulate a contact-impact event such as car crash or metal forming. Traditionally, shell elements (i.e., flat surfaces) are used in FEA to represent a master segment used for contacts, for example, triangle or quadrilateral. In an impact event, two portions of a structure are in contact with each other. Using flat surfaces to approximate a curved geometry creates a problem in simulation such event. Finite element discretization of such surface generally needs high mesh density (i.e., very fine mesh) for curved geometry, this leads to an unnecessarily large and complex FEA model hence requiring long computations for the simulation.
Additionally, the computer simulated contact is based on an algorithm including a master segment and a slave node to represent the two contact portions of the structure. Using a flat segment to approximate a curved surface could cause another problem. The simulated contact would occur only when the approximated flat portion of a master segment is in contact with a slave node. But the physical contact between two portions of the structure may have already occurred because the curvature of the surface had not been considered in prior art approach, or vice versa. As a result, the approximation of using flat segment to approximate curved surface can generate different or sometimes erroneous results, thus leads to incorrect conclusion regarding the integrity of the structure.
Furthermore, prior art approach has yet another problem with respect to discontinuity of the surface normal at the intersection or node shared with several master segments due to different slopes. As a result, the discontinuity could cause numerical inaccuracy or an interface not including all nodes from the input geometry. Therefore, it would be desirable to have an improved method of creating a contact-impact interface in a finite element analysis that overcomes shortcomings, drawbacks and problems of the prior art approaches.